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Quantum Physics

Title:The decoupling approach to quantum information theory

Abstract: Quantum information theory studies the fundamental limits that physical laws
impose on information processing tasks such as data compression and data
transmission on noisy channels. This thesis presents general techniques that
allow one to solve many fundamental problems of quantum information theory in a
unified framework. The central theorem of this thesis proves the existence of a
protocol that transmits quantum data that is partially known to the receiver
through a single use of an arbitrary noisy quantum channel. In addition to the
intrinsic interest of this problem, this theorem has as immediate corollaries
several central theorems of quantum information theory. The following chapters
use this theorem to prove the existence of new protocols for two other types of
quantum channels, namely quantum broadcast channels and quantum channels with
side information at the transmitter. These protocols also involve sending
quantum information partially known by the receiver with a single use of the
channel, and have as corollaries entanglement-assisted and unassisted
asymptotic coding theorems. The entanglement-assisted asymptotic versions can,
in both cases, be considered as quantum versions of the best coding theorems
known for the classical versions of these problems. The last chapter deals with
a purely quantum phenomenon called locking. We demonstrate that it is possible
to encode a classical message into a quantum state such that, by removing a
subsystem of logarithmic size with respect to its total size, no measurement
can have significant correlations with the message. The message is therefore
"locked" by a logarithmic-size key. This thesis presents the first locking
protocol for which the success criterion is that the trace distance between the
joint distribution of the message and the measurement result and the product of
their marginals be sufficiently small.